unit cube Activity4 by Ms. Rashmi Kathuria

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This is an activity to verify the cubic algebraic formula for
a^3+b^3.

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unit cube Activity4 by Ms. Rashmi Kathuria

  1. 1. Algebraic Identities… By RASHMI KATHURIA
  2. 2. Activity 4 <ul><li>Aim : To prove the algebraic identity </li></ul><ul><li>a 3 +b 3 =(a+b)(a 2 -ab+b 2 ) </li></ul><ul><li>using unit cubes. </li></ul><ul><li>Material required: Unit Cubes. </li></ul>
  3. 3. Start Working.. Take any suitable value for a and b. Let a=3 and b=1
  4. 4. Step 1. To represent (a) 3 make a cube of dimension a x a x a i.e. 3x3x3 cubic units.
  5. 5. Step2. To represent (b) 3 take a cube of dimension b x b x b i.e. 1x1x1 cubic units.
  6. 6. Step3. To represent a 3 +b 3 add a cube of dimension b x b x b i.e. 1x1x1 to the cube formed in the step 1 of dimension a x a x a i. e 3x3x3 cubic units. + =
  7. 7. Step4. To represent (a+b)a 2 make a cuboid of dimension (a +b) x a x a i.e. 4x3x3 cubic units.
  8. 8. Step5. To represent (a+b)a 2 +(a+b)b 2 add a cuboid of dimension (a +b) x b x b i. e 4 x1 x 1 to the cuboid formed in the previous step.
  9. 9. Step6. To represent (a+b)a 2 +(a+b)b 2 -(a+b)ab extract a cuboid of dimension (a+b) x a x b i.e. 4x3x1 cubic units from the shape formed in the previous step..
  10. 10. Step7. Rearrange the unit cubes left to form the shape formed in the Step 3.
  11. 11. Observe the following <ul><li>The number of unit cubes in a 3 = …27….. </li></ul><ul><li>The number of unit cubes in b 3 = …1….. </li></ul><ul><li>The number of unit cubes in a 3 +b 3 = …28….. </li></ul><ul><li>The number of unit cubes in (a+b)a 2 =…36…… </li></ul><ul><li>The number of unit cubes in (a+ b) a b=…12…… </li></ul><ul><li>The number of unit cubes in (a+b)b 2 =…4…… </li></ul><ul><li>The number of unit cubes in (a+b)a 2 _ (a+ b) a b + (a+b)b 2 </li></ul><ul><li>= …28…… </li></ul>
  12. 12. It is observed that the number of unit cubes in a 3 +b 3 is equal to the number of unit cubes in (a+b)a 2 -(a+b)ab+(a+b)b 2 i.e. (a+b)(a 2 -ab+b 2 ). Learning Outcome
  13. 13. Acknowledgement <ul><li>I would like to thank my sister who has helped me to click these picture from the mobile and then transferring to the computer. </li></ul>
  14. 14. Thank You

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